Finite Group Databasebeta

← C11×#11993 #14589186

Subgroups — C11×#11993 #14589186

Order 2816.

360 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3152C211yesmaximal, characteristic
2C11×#2165C212yesmaximal, complemented
3C11×#1359C212yesmaximal, complemented
4C11×#1358C212yesmaximal, complemented
5C2×C11×#137—22no—
6C11×#532C411yescharacteristic
7C2×C11×C4⋊Q8C411yescharacteristic
8C11×#497—22no—
9C11×#494C411yescharacteristic
10C11×#494C2211yescharacteristic
11C11×#492C411yescharacteristic
12C11×#492C2211yescharacteristic
13C4×C11×M16C2211yescharacteristic
14C11×#364C2214yes—
15C11×#349—22no—
16C11×#347—22no—
17C2×C11×#41—21no—
18C22×Q8×C11—21no—
19C11×#137—48no—
20C2×C11×Q16—22no—
21C2×C11×Q16—22no—
22C2×C11×SD16—22no—
23C2×C11×SD16—22no—
24C2×C11×M16D412yes—
25C11×C4⋊Q8—21no—
26C11×C4⋊Q8—41no—
27C11×C4⋊Q8C2×C411yescharacteristic
28C11×C4⋊Q8C2×C411yescharacteristic
29C11×C4⋊Q8C2×C411yescharacteristic
30C11×#127C2×C411yescharacteristic
31C11×#124—21no—
32C11×#121—41no—
33C4×D4×C11—41no—
34C2×C11×C4⋊C4—41no—
35C2×C42×C11C2×C411yescharacteristic
36C11×M32—24no—
37C11×#97D412yes—
38C4×C8×C11C2×C411yescharacteristic
39C4×C8×C11C2311yescharacteristic
40#11993C1111yesmaximal, characteristic, direct product factor, Sylow
41C11×#41—44no—
42C2×Q8×C11—21no—
43C2×Q8×C11—21no—
44C2×Q8×C11—21no—
45C2×Q8×C11—44no—
46C2×Q8×C11—41no—
47C2×D4×C11—21no—
48C2×D4×C11—41no—
49C2×D4×C11—41no—
50C22×C4×C11—21no—
51C22×C4×C11—41no—
52C22×C4×C11—41no—
53C22×C4×C11C22⋊C411yescharacteristic
54C11×Q16—44no—
55C11×Q16—44no—
56C11×SD16—44no—
57C11×SD16—44no—
58C11×M16—24no—
59C2×C8×C11C22⋊C412yes—
60C2×C8×C11C2×D412yes—
61C11×C4⋊C4—42no—
62C11×C4⋊C4—41no—
63C11×C4⋊C4—41no—
64C11×C4⋊C4—41no—
65C11×C22⋊C4—42no—
66C42×C11—21no—
67C42×C11C22⋊C411yescharacteristic
68C42×C11C22×C411yescharacteristic
69C11×C16—44no—
70#3152C2×C1111yescharacteristic
71#2165C2×C1112yescomplemented
72#1359C2×C1112yescomplemented
73#1358C2×C1112yescomplemented
74C23×C11—41no—
75C23×C11#10011yescharacteristic
76Q8×C11—42no—
77Q8×C11—42no—
78Q8×C11—42no—
79Q8×C11—82no—
80D4×C11—42no—
81D4×C11—82no—
82D4×C11—82no—
83C2×C4×C11—21no—
84C2×C4×C11—22no—
85C2×C4×C11—21no—
86C2×C4×C11—42no—
87C2×C4×C11—41no—
88C2×C4×C11—41no—
89C2×C4×C11—41no—
90C2×C4×C11—82no—
91C2×C4×C11—82no—
92C2×C4×C11#10011yescharacteristic
93C2×C4×C11C2×C22⋊C411yescharacteristic
94C8×C11—22no—
95C8×C11AGL(1,ℤ/8)14yes—
96C2×#137—22no—
97#532C4×C1111yescharacteristic
98C2×C4⋊Q8C4×C1111yescharacteristic
99#497—22no—
100#494C4×C1111yescharacteristic
101#494C22×C1111yescharacteristic
102#492C4×C1111yescharacteristic
103#492C22×C1111yescharacteristic
104C4×M16C22×C1111yescharacteristic
105#364C22×C1114yes—
106#349—22no—
107#347—22no—
108C22×C11—21no—
109C22×C11—41no—
110C22×C11—82no—
111C22×C11—81no—
112C22×C11C2×#10011yescharacteristic
113C4×C11—22no—
114C4×C11—21no—
115C4×C11—41no—
116C4×C11—81no—
117C4×C11—81no—
118C4×C11—81no—
119C4×C11#41812yes—
120C2×#41—21no—
121C22×Q8—21no—
122#137—48no—
123C2×Q16—22no—
124C2×Q16—22no—
125C2×SD16—22no—
126C2×SD16—22no—
127C2×M16D4×C1112yes—
128C4⋊Q8—21no—
129C4⋊Q8—41no—
130C4⋊Q8C2×C4×C1111yescharacteristic
131C4⋊Q8C2×C4×C1111yescharacteristic
132C4⋊Q8C2×C4×C1111yescharacteristic
133#127C2×C4×C1111yescharacteristic
134#124—21no—
135#121—41no—
136C4×D4—41no—
137C2×C4⋊C4—41no—
138C2×C42C2×C4×C1111yescharacteristic
139M32—24no—
140#97D4×C1112yes—
141C4×C8C2×C4×C1111yescharacteristic
142C4×C8C23×C1111yescharacteristic
143C2×C11—21no—
144C2×C11—41no—
145C2×C11—161no—
146C2×C11#155511yescharacteristic
147#41—44no—
148C2×Q8—21no—
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—44no—
152C2×Q8—41no—
153C2×D4—21no—
154C2×D4—41no—
155C2×D4—41no—
156C22×C4—21no—
157C22×C4—41no—
158C22×C4—41no—
159C22×C4C11×C22⋊C411yescharacteristic
160Q16—44no—
161Q16—44no—
162SD16—44no—
163SD16—44no—
164M16—24no—
165C2×C8C11×C22⋊C412yes—
166C2×C8C2×D4×C1112yes—
167C4⋊C4—41no—
168C4⋊C4—41no—
169C4⋊C4—41no—
170C4⋊C4—42no—
171C22⋊C4—42no—
172C42—21no—
173C42C11×C22⋊C411yescharacteristic
174C42C22×C4×C1111yescharacteristic
175C16—44no—
176C11#1199311yescharacteristic, direct product factor, Sylow
177C23—41no—
178C23C11×#10011yescharacteristic
179Q8—42no—
180Q8—42no—
181Q8—42no—
182Q8—82no—
183D4—42no—
184D4—82no—
185D4—82no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—42no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—82no—
194C2×C4—82no—
195C2×C4C11×#10011yescharacteristic
196C2×C4C2×C11×C22⋊C411yescharacteristic
197C8—22no—
198C8C11×AGL(1,ℤ/8)14yes—
199C22—21no—
200C22—41no—
201C22—82no—
202C22—81no—
203C22C2×C11×#10011yescharacteristic
204C4—22no—
205C4—21no—
206C4—41no—
207C4—81no—
208C4—81no—
209C4—81no—
210C4C11×#41812yes—
211C2—21no—
212C2—41no—
213C2—161no—
214C2C11×#155511yescharacteristic
subgroupG/H
center, socleC2×C11#1555
commutatorC42C22×C4×C11
Frattini, cosocleC4×C8C23×C11
prime radicalC11×#532C4
LCSG ▷ C42 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C11 ◁ C2×C4×C11 ◁ C4×C11×M16 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C11×#2165C2semidirect
3. C11×#1359C2semidirect
4. C11×#1358C2semidirect
40. #11993C11direct (N × H)
71. #2165C2×C11semidirect
72. #1359C2×C11semidirect
73. #1358C2×C11semidirect
176. C11#11993direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C11×#31522
C11×#21652
C11×#13592
C11×#13582
#1199311